Structural models with qualitative values

In fields of study from cognition to organizations and social networks , empirical structures have been formally represented in terms of graph theoretical models. When the empirical relationships can be seen as valued, a valued graph or digraph is called for. Values have been conventionally identified with real numbers, but other sorts of entities (most often signs) have been used. In this paper, we demonstrate a general system under which graphs and digraphs with values that are not numbers may be used to represent various important properties and features of empirical structures. Special cases include multiplexity of relationships, formal and informal linkages in organizational structures, systems and their environments, and structural consistency principles. The general system incorporates a matrix methodology which permits the convenient analysis of empirical structures. These cases are also intended to exemplify the ways in which valued relational models may be developed to extend this kind of formalization and its methodology to other areas of substantive interest.     

A new model and a hyper-heuristic approach for two-dimensional shelf space allocation

In this paper, we propose a two-dimensional shelf space allocation model. The second dimension stems from the height of the shelf. This results in an integer nonlinear programming model with a complex form of objective function. We propose a multiple neighborhood approach which is a hybridization of a simulated annealing algorithm with a hyper-heuristic learning mechanism. Experiments based on empirical data from both real-world and artificial instances show that the shelf space utilization and the resulting sales can be greatly improved when compared with a gradient method. Sensitivity analysis on the input parameters and the shelf space show the benefits of the proposed algorithm both in sales and in robustness.     

Ernst Kleinert: Mathematische Modelle des Kontinuums

Mathematische Semesterberichte -